Composition of Transformations

Abstract

Let X be any set. A mapping of X into itself is called a transformation of X. Since a transformation is a special case of a mapping of sets, we will naturally retain the terminology and notation of Chapter 1.2, with one difference. By convention we will denote transformations by lower-case Greek letters, and elements of the set by lower-case Roman letters. In particular, if α maps x onto y, then y will be called the image of x under α, and we write αx = y or α(x) = y.